Generalized Confidence Intervals for Process Capability Indices of Log-normal Distribution in the One-way Random Model

Traditional process capability indices require that quality characteristics follow normal distribution. But in the actual production processes, quality characteristic usually has a non-normal distribution and almost all the production processes exhibit the between batch variability besides the within batch variability. This paper proposed confidence intervals for process capability indices for log-normal process under the one-way random model based on the generalized confidence interval. Motivated by the generalized confidence intervals, the confidence interval of the process capability indices of log-normal distribution are constructed based on the one-way random model. The good performance of generalized lower confidence limits and its coverage probabilities are studied via simulation, and simulation results show the good performance of the generalized confidence interval method in the log-normal distribution case. Finally, examples are provided to illustrate the implementation of the proposed method.